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Graphing Dilations in the Coordinate Plane

Learn how to graph dilations in the coordinate plane using a center point and scale factor. Practice dilating polygons and finding the scale factor and center of a dilation.

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Graphing Dilations in the Coordinate Plane

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  1. 9.6: Dilations I can draw dilations in the coordinate plane.

  2. If the images to the right describe a dilation, in your own words, define dilation:

  3. Vocabulary! A dilation or scaling is a similarity transformation that enlarges or reduces a figure proportionally with respect to a center point and a scale factor. To find the coordinates of an image after a dilation centered at the origin, multiply the x- and y-coordinates of each point on the preimage by the scale factor of the dilation, k. The ratio of a length on an image to a corresponding length on the preimage.

  4. Example 1: Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), G(8, 4) and H(–4, –8). Graph the image of EFGH after a dilation centered at the origin with a scale factor of 1/4.

  5. Example 2a: Find the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor. J(2, 4), K(4, 4), P(3, 2); r= 2

  6. Example 2b: Find the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor. D(–2, 0), G(0, 2), F(2, –2) r= 1.5

  7. Example 3: Leila drew a polygon with coordinates (–1, 2), (1, 2), (1, –2), and (–1, –2). She then dilated the image and obtained another polygon with coordinates (–6, 12), (6, 12), (6, –12), and (–6, –12). What was the scale factor and center of this dilation?

  8. Example 4: Find the scale factor from the pre-image to the image for the following dilation. A(2,5), B(3,-1), C(4,2) and A’(3, 7.5), B’(4.5, -1.5), C‘(6, 3).

  9. Summary! Nemo is located on the coordinate plane. Write down Nemo’s coordinate points here: Marlin believes Nemo will be 3 times the size he is now. Dilate the Nemo using a scale factor of 3. Write the coordinate points here: Graph the dilated coordinate points and name them accordingly. When you are finished, compare with your neighbor.

  10. Homework: pg. 678, #15 – 17, 21, 26

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